I always hate to try to describe this on the web, cause it really needs to be worked on with a teacher and very slowly to make sure you have a firm foundation before moving on to the next exercise.
First let me say that I think working with a nome is more valuable than working with a drum machine (unless you set the drum machine just to play on 2 and 4 or all quarters). The reason it's "more interesting" to work with a Dm than a nome is precisely what's kind of bad about it. With a nome you only have your improvised line to move the tune forward. You become much more aware of how note choice (and not just rhythm) affects the harmonic propulsion of a tune.
Anyway, you put the nome so 60bpm=quarternote and, after using the REALLY LEARNING A TUNE (meldoy and chord line) you start improvising with the following parameters.
A. 1 chorus melody, 1 chorus "chord line", improvise 1 chorus of half notes (trying to maintain the sense of melody rather than accompaniment) , 1 chorus of melody
B. 1 chorus melody, 1 chorus in the following manner - for each 8 bar section play the melody for the first three bars, then improvised half note line for the other 5 bars, 1 chorus melody
C. 1 chorus melody, 1 chorus in the following manner - for each 8 bar section, play 3 bars of melody in a different place for each section. In other words if you play the melody for the first 3 bars of the first 8 bar section, you MAY NOT play the melody in the first three bars of any other 8 bar section. Clear? You improvise the other 5 bars in half notes.
D. 1 chorus melody, 1 chorus in the following manner - improvise half note lines with rests. The number of beats in a rest should roughly equal the number of bars improvised in half notes.
Then you go through B to D and start changing the rhythmic unit of improvised line -
1.from half notes to quarter notes
2.from quarter notes to "no accent" 8th notes
3. to "accent 1" 8th notes accenting the first note of each group of 4 (1 & 2 & 3 & 4 & 1 &
4.to "accent 2" 8th notes (1 &2 & etc
5. to accent 3 8th notes
6. to accent 4 8th notes
7. to no accent triplets
8. to accent 1 triplets
9. to accent 2 triplets
10. to accent 3 triplets
11. to no accent 16th notes
12. you know the drill - accent 1 through accent 4 16th notes
By the end of this you should be able to take an improvised line and start it anywhere in the bar, end it anywhere in the bar, with any accent/phrasing you want. You also get the visceral feeling of what improvising against a constant feels like. You couple these with exercises where you just turn on the nome and blow through tunes, you really start solidifying your time feel in a physical way, you start hearing time as a steady stream that you can drop your line in and out of at YOUR will. Rather than something that you've got to hang on to for dear life.
I keep the click on when working on arpeggiation exercises, scale work, melodic fragments as well.